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Get the right product (Posted on 2015-12-01) Difficulty: 3 of 5
For a positive integer n > 2, consider the n-1 fractions 2/1; 3/2; ...; n/(n-1).

The product of these fractions equals n, but if you reciprocate (i.e. turn upside down) some of the fractions, the product will change.

How can you make the product equal 1?
Find all values of n for which this is possible.

No Solution Yet Submitted by Ady TZIDON    
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Solution Different solution | Comment 2 of 5 |
Paul gave the solution for n=4:  1/2*3/2*4/3=1
notice the primes.  2 and 2 cancel the 4 and the 3's cancel each other.
If you go to n=5 you introduce a new prime that does not cancel, you'd need to increase n to 10 to get another 5 but this just introduces more primes (7), each of which will have the same problem.  Since between any prime p and 2p there is another prime (thanks Erdös), no higher n will work.

  Posted by Jer on 2015-12-02 07:18:54
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